// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Eigenvalues>
#include <limits>

template<typename MatrixType>
void
schur(int size = MatrixType::ColsAtCompileTime)
{
	typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
	typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;

	// Test basic functionality: T is triangular and A = U T U*
	for (int counter = 0; counter < g_repeat; ++counter) {
		MatrixType A = MatrixType::Random(size, size);
		ComplexSchur<MatrixType> schurOfA(A);
		VERIFY_IS_EQUAL(schurOfA.info(), Success);
		ComplexMatrixType U = schurOfA.matrixU();
		ComplexMatrixType T = schurOfA.matrixT();
		for (int row = 1; row < size; ++row) {
			for (int col = 0; col < row; ++col) {
				VERIFY(T(row, col) == (typename MatrixType::Scalar)0);
			}
		}
		VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
	}

	// Test asserts when not initialized
	ComplexSchur<MatrixType> csUninitialized;
	VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
	VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
	VERIFY_RAISES_ASSERT(csUninitialized.info());

	// Test whether compute() and constructor returns same result
	MatrixType A = MatrixType::Random(size, size);
	ComplexSchur<MatrixType> cs1;
	cs1.compute(A);
	ComplexSchur<MatrixType> cs2(A);
	VERIFY_IS_EQUAL(cs1.info(), Success);
	VERIFY_IS_EQUAL(cs2.info(), Success);
	VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
	VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());

	// Test maximum number of iterations
	ComplexSchur<MatrixType> cs3;
	cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
	VERIFY_IS_EQUAL(cs3.info(), Success);
	VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());
	VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());
	cs3.setMaxIterations(1).compute(A);
	VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);
	VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);

	MatrixType Atriangular = A;
	Atriangular.template triangularView<StrictlyLower>().setZero();
	cs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
	VERIFY_IS_EQUAL(cs3.info(), Success);
	VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());
	VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));

	// Test computation of only T, not U
	ComplexSchur<MatrixType> csOnlyT(A, false);
	VERIFY_IS_EQUAL(csOnlyT.info(), Success);
	VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
	VERIFY_RAISES_ASSERT(csOnlyT.matrixU());

	if (size > 1 && size < 20) {
		// Test matrix with NaN
		A(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
		ComplexSchur<MatrixType> csNaN(A);
		VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
	}
}

EIGEN_DECLARE_TEST(schur_complex)
{
	CALL_SUBTEST_1((schur<Matrix4cd>()));
	CALL_SUBTEST_2((schur<MatrixXcf>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
	CALL_SUBTEST_3((schur<Matrix<std::complex<float>, 1, 1>>()));
	CALL_SUBTEST_4((schur<Matrix<float, 3, 3, Eigen::RowMajor>>()));

	// Test problem size constructors
	CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
}
